Fire Resistance of Unprotected Ultra Shallow Floor Beams (USFB): A Numerical Investigation

This paper presents the fire resistance behaviour of partially encased in concrete ultra shallow floor beams (USFB) using numerical analysis method based on material specifications of the EN1994-1-2. Investigating the behaviour of USFBs under elevated temperatures is crucial in determining their fire resistance and evaluating their overall performance in contemporary construction. Even though the manufacturing company provides fire resistances for USFBs based on EC4-1-2 procedures, their response to elevated temperature effects remains up to date neither well documented nor clearly understood. The analyses involved two different beams of span 5 m and 8 m respectively, as specified by the manufacturer. Analysis results showed that such beams, when unprotected, experience severe temperature gradients if exposed to fire, as the lower flange still remains unprotected in contrast to the concrete encased part of the cross-section. As it was anticipated, the moment capacity governs the fire resistance of the beams and the load factor highly effects the elevated temperature behaviour. In addition, the loss of the lower flange, which develops high temperatures, is not compensated by the web and consequently the moment capacity ultimately depends on the temperature of the lower flange. Results also suggest that simulated beams sustained the applied load for approximately 40 min of exposure to the standard fire.


Introduction
Various shallow floor systems have been developed recently.The most commonly encountered in the industry are the "slim floor" and the "slim deck" systems.Several companies have developed their own systems, such as the Ultra Shallow Floor Beams (USFB) composite deck system [1].The behavior of such flooring systems when exposed to fire is generally satisfactory, because the encasing concrete acts as thermal insulation, even though the lower flange is unprotected.The results of relevant parametric analyses [2], [3], [4] have shown that the fire resistance of such shallow systems is governed by deflection, because they experience bowing resulting from considerable thermal gradients.
In spite of the fact that the fire behavior of slim floor and slim deck systems has been investigated by various researchers [2], [5] to [10], systems proposed by other manufacturing companies, such as the USFBs [1], have not been sufficiently studied at elevated temperatures.The USFBs seem to exhibit significantly different behavior than these systems (which generally have a satisfactory fire resistance) as they use short sections which are protected less by the concrete [2] while the web, which has to develop stresses after the capacity loss of the lower flange, in order to develop a moment capacity, is perforated.Despite this, the manufacturing company certifies (based on EC4-1-2 [12] procedures) for each beam the appropriate fire insulation.Due to the absence of vital information for evaluating the Eurocodes procedures for the specific system and the fact that experimental results are not available, the authors conducted a numerical simulation of such USFB systems exposed to fire.For this purpose, Finite Element (FE) analyses with the commercial program ABAQUS were carried out.The methodology used in the current USFB analysis is similar to the model used in the analysis of asymmetric slim floor beams in fire and published by Maraveas et al [2].
Two commonly used simply supported isolated USFBs have been analysed.The considered span lengths are 5m and 8m, with shape and arrangement described in section 2. Additional checks were made to determine the performance of the section in fire and ensure that the serviceability limit state stresses were not excessive as described in the estimated by the manufacturer's available software [1].Table 1 shows the normal temperature maximum design unity factors and the critical load combination for the considered two beams.The calculations performed with the software Cellbeam v9.0 (certified by the Steel Construction Institute).The bolded values in Table 1 refer to the critical code checks/verifications according to a modified EC4 design procedure proposed by the SCI and used internally by ASD Westok (RT1371).

USFB system
For conventional composite floor beams or down stand composite beams, the thickness of the flanges increases with the increase in span.Consequently, the steel sections are often heavier than needed.The USFB is a new type of composite floor beam, which is fabricated by welding two highly asymmetric cellular tee-sections together along the web.Profiled steel decking or precast concrete floor units sit on the bottom flange, as shown in Figure 1 and 2. The top and bottom tee-sections are cut from different parent plain beams where the top tee-section is much smaller than the bottom tee-section.This asymmetric beam section property reduces the self-weight while increases the moment capacity.
USFB provides superior structural performance [13] due to the concrete infill where the ultimate vertical load carrying capacity of the USFB can increase by up to 108% compared to the corresponding non-composite perforated steel beam.Moreover, the shear resistance of the USFB, without using any mechanical shear connectors, such as shear studs, re-bars and ducting [14] can be provided mainly by contributions from the concrete confinement and the steel flange thickness.The strut action of the concrete confinement through the web openings reduces the Vierendeel bending effects and improves the vertical shear transfer in the vicinity of the web openings.In addition, it was demonstrated that there is some residual strength in the concrete preventing local buckling of the perforated steel beams and the load carrying capacity is somewhat higher than that on the noncomposite beam.
The circular or elongated web openings provide a channel for reinforcing tie-bars, building services and ducting through the structural depth of the beam, thus minimizing the overall floor depth [14].Transverse to the web reinforcing tie-bars can provide longitudinal shear strength by tying the concrete on both sides of the web.Shear studs can be also used, welded horizontally on the web of the steel beams.Full service integration can be achieved when deep profiled steel decking is employed, as pipes or ducks pass through between the ribs of the steel decking, and typically every a few web openings which are not filled by concrete.As the floors are cast, the in-situ concrete passes through most web openings, which may or may not include a tie-bar or duct.In the case of ultra-shallow precast units, all web openings are filled by in-situ concrete, hence service integration is not provided, as opposed to the profile metal decking use.This concrete plug forms a unique enhanced mechanism for transferring longitudinal shear force along the beam.
The common range of application for USFBs is for slab depths of 180 to 300mm, in which the concrete is placed flush with the upper flange.The nature of the choice of UC for the bottom tee-sections and UB for the top tee-sections is that the asymmetry in flange areas can be over 3 to 1. Composite action reduces this effective asymmetry and improves the bending resistance.In practice, the span to depth ratio of USFBs is generally in the range of 25 to 30, which means that serviceability rather than bending or shear resistance will govern.Another study has been conducted on the derivation of dynamic properties of USFBs through FE modal analysis and experimental verification [15] and [16].3. Geometry, Loads and Material Properties 3.1.

Geometry of studied systems and normal temperature design
In this paper, two typical simply supported USFBs have been analyzed.The first (beam A) (Figure 3a), has a total section height of 220mm and the steel section is comprised of an upper UB254x146x37 tee-section and a lower UC305x305x97 tee-section.The second (beam B) (Figure 3b), has a total section height of 275.2mm and the steel section is comprised of an upper UC254x254x167 teesection and a lower UC356x406x235 tee-section.Both have 100mm diameter holes in their web, at an axial distance of 300mm between them.The slabs are made of C30/37 concrete and are manufactured with pre-cast units.The span of beam A is 5m and of beam B 8m.The effective width (b eff ) has been taken equal to L/8, where L is the span.The design data at normal temperatures is presented in Table 1.As it is evident, the design is at the limit and there is no over strength that would have affected the results.

Applied loads
The main load combination for ambient temperature design according to EN1991 [17] is generally: Which gives a total applied force of 332.55kN for beam A and 452.15kN for beam B. For fire design, the main load combination according to EN1991 is: Where: ψ 2 obtains various values depending on the type of the structure and always ψ 2 <1.As it is not possible to determine the result of the combination with these unknown, it has been assumed that ψ 2 =1.The fire design combination results for these safety factors are approximately 70% of those of the ambient temperature design combination, which is the maximum load that can be required for fire design.The load is uniformly distributed along the length of each beam.

Thermal properties and thermal expansion
The thermal properties, such as the specific heat and thermal conductivity, of the structural steel and concrete used are given by EC4-1-2 [12].Especially for the concrete, the upper bound of the curve of thermal conductivity was used.
Respectively, the thermal expansion of the two materials was obtained by the same Specification.A density of 7850kg/m 3 was taken for structural steel, and of 2300kg/m 3 for concrete.

Mechanical properties
The mechanical properties of the materials were obtained by the EN1994-1-2 [12].In particular, the stress-strain-temperature diagrams are presented at

Finite Element (FE) modeling
FE modeling of the USFBs is performed with eight-node hexahedral solid elements (Figure 5) taking into consideration the interface between the steel section and surrounding concrete through appropriate thermal and mechanical contact properties, with the reinforcing bars (shear connection system) modeled as well for estimating the structural response.Due to symmetry, only one quarter of the composite beam is modeled using appropriate boundary and load conditions.The thermal response of the model is calculated via transient uncoupled heat transfer analysis and the structural response via non-linear static analysis performed in two steps.In the first step, the composite beam is subjected to static loads at ambient temperature.In the second step, the composite beam is heated using the temperatures predicted by the heat transfer analysis with the previous static loads remaining (transient-state test method).Three-dimensional (3D) heat transfer elements (DC3D8, 8-node linear bricks) are used for estimating the thermal response of the USFB beams.The temperature distribution in the composite beam is predicted based on the standard fire curve (ISO 834) [18].A convection coefficient of 25W/m 2 K is assumed for the exposed surface and 9W/m 2 K for the unexposed one.The radiation emissivity for the lower steel flange is taken to be 0.5 and for the concrete floor 0.25.The heat flow due to radiation is neglected for the upper side.The interface conductivity between concrete and steel is considered as infinite (perfect thermal contact).No heat is transferred normally to the symmetry axes.Heat is applied to the bottom surface of the composite beam and the radiation within the holes of the pre-casted slabs has been considered.Figure 6 presents the thermal analysis boundary conditions.

Structural analysis
Three-dimensional (3D) solid elements are used for estimating the structural response of USFB structural systems.The concrete slab is modeled with 8-node linear brick elements (C3D8) due to numerical instabilities associated with the inelastic behavior of concrete.On the other hand, the steel beam is modeled with brick elements enhanced with incompatible modes (C3D8I) which provide accurate results [2].All the nodes on the symmetry surfaces are prevented to move in the perpendicular direction.Steel nonlinear behavior is modeled with the von Mises plasticity model, whereas concrete nonlinear behavior is modeled using the damaged plasticity model in combination with hardening and stiffening options with a dilation angle equal to 55° for numerical reasons that Abaqus' solver was unstable for the concrete dilatation angle between 15-30 o .To solve this stability issue, very small time increments were employed.It was then resulted that the use of 55 o angle did improve the stability of the analysis without further effects on the analysis results.
Reinforcing bars are modeled via the *REBAR option of Abaqus [19], while they do not participate in the heat transfer analysis.The interaction between concrete and steel is modeled with the *CONTACT PAIR option of Abaqus.A friction coefficient equal to 0.50 is considered for the tangential behavior of the interfaces using the isotropic Coulomb friction model.At final, geometric nonlinearities are considered during the analysis.

Validation of FE models
The FE models have been validated against slim floor fire tests as presented by Maraveas et al. [2].The slim floors share common characteristics with the USFBs.Yet, there are a few parts that have not been validated previously, as they do not exist at slim floors are as follow: -The pre-cast slabs; hence it is unknown if the heat transfer model between steel and pre-cast concrete is accurate.
-The shear connection system; namely the reinforcement bars that cross through the web openings.
It is estimated that the above parts of the system do not significantly affect the analyses presented in this paper, and this because of the organic form of construction (Figures 1 and 2) indicating how the effective area of concrete is acting with the USFB.Therefore, no substantial slip between steel beam and concrete is expected.

Thermal analysis
The results of thermal analysis have been presented in Figure 7, 8 and 9.The exposed bottom flange of the steel cross-section develops high temperatures.For beam A, due to low thickness the temperature is almost uniform except of the area near the web (nodes 1 and 2, Figure 8b), where the temperatures are lower as the web is getting heated.For beam B, the thick bottom flange is heated slowly and the temperature is not uniform (nodes 1 to 6, Figure 9b).The transport of heat on the concrete surface (node 5) is affected by the heat coming from the steel flange at one side and the ISO fire curve at the bottom part.Also, due to the low thermal conductivity of concrete, the temperature at node 5 is higher than the temperature at node 1 (at bottom flange).As the thermal conductivity of steel is high, the web is getting hot too.The temperature at the mid-point of the web exceeds the 400 o C after 110min of exposure (node 2).The upper flange is not practically affected (node 3) and it is not exceeding the 120 o C even after 120min of exposure.The temperature of the reinforcement (node 6) is always very low as it is well insulated from the concrete.The insulated by concrete web openings are affecting the temperature distribution.The bottom edge of the opening (node 4) is developing temperatures near the 600 o C at 60min of exposure although the upper edge of the openings is generally experienced low temperatures (Figure 7c).The web openings inside the pre-cast slab demonstrate similar effects (Figure 7b).

Structural analysis
The results from the structural analysis are presented in Figure 10.It transpires that the limit of L/20 for the mid-span deflection and deflection rate limit of L 2 /(9000d) is exceeded in about 40min at both beams.It should be noted that the excess of the deflection rate limit is equivalent to the lost of the load bearing capacity.Both beams also fail in bending at about 40min of standard fire exposure.The effect of the load factor is important as the beams may have improved fire resistance for reduced load factors (R60+).
From these results it is apparent that fire resistance is governed by the thermal expansion of the lower flange, which develops very high temperatures contrary to the rest of the section.The developing thermal gradients lead to beam bowing and large deflections, which limit the fire resistance.

Sensitivity analysis
In order to access the uncertainties of the used numerical model, a sensitivity analysis has been performed for the parameters presented in Table 2.In every analysis only one parameter according Table 2 was modified, so eight analyses for each beam were performed.The effect of these parameters has been presented in Figure 10 as error bars.The differences observed are minor and they do not affect the overall behaviour.

Assessment of EC4-1-2 procedure
According to Westok calculations performed by CELLBEAM v.9.0 software [20], the critical temperatures according to EC4-1-2 [12]  As it was presented in Section 5.1, the lower flange temperature is always higher than the web temperature.Thus, the lower flange temperature governs the fire resistance of USFBs. Figure 11 realizes the displacements, obtained from the presented FE analysis, as a function of the lower surface flange temperature (node 1).From Figure 11, it is evident that EC4-1-2 [12] gives satisfactory results, for both beams it gives rather conservative results, as beam A fails at 300 o C higher temperature than EC4-1-2 predictions and beam B fails at almost 200 o C higher temperature than the respected EC4-1-2 predictions.In any case, EC4-1-2, though not particularly accurate, seems to be on the side of safety.

Effect of fire on the moment capacity of USFBs
When a steel-concrete composite beams is in equilibrium, the part of the steel section that is in tension produces a force equal to the resultant force of the concrete compressive stresses (to which are included the compressive stresses of the upper flange of the steel section and the reinforcement bars that nevertheless do not govern the behavior as strains are limited by the concrete), as it appears in Figure 12a.When the steel section has a hole in the web, the tensile force is produced from the bottom tee-section, and it is equal to its surface area multiplied by the yield strength, is reduced by a corresponding safety factor (Figure 12b).When a non-uniform temperature profile, with temperatures generally larger than 400 o C, is applied on the section and particularly at the bottom tee-section, the yield strength is reduced.This mainly occurs at the lower flange which exhibits the highest temperatures and produces (proportionally to its surface area and lever arm) the largest part of the moment capacity.The reduction of stresses at the lower flange cannot be partially covered by increasing the stresses at the web, as usually occurs in uniform sections [11], as the web is absent for the most part along the length of the beam.However, it has to be noted, that part of the tensile force reduction at the section is counterbalanced by the change of the material safety factor for fire design and the change in position of the neutral axis which increases the lever arm (Figure 12c).
As it can be seen in Figure 8a, at about 40min (Figure 10a), when beam A fails, the mean temperature of bottom Tee is about 555 ο C, which corresponds to the yield strength with a reduction factor of 0.60 when the loads are taken reduced by 70% compared to the normal temperature design combination.
Respectively, regarding the beam B, failure results at about the same time (Figure 10b) and the mean temperature of bottom Tee is 535 ο C (Figure 9b), which corresponds to the yield strength with a reduction factor of 0.67.
Furthermore, improving the accuracy of the results, the average temperature of the bottom flange and bottom part of web should be calculated separately as well as consider the reduction of yield strength for each one separately.
Using the standard fundamental conditions of equilibrium, the plastic analysis at the neutral axis can be calculates as: Where A i is the area of each fiber i of steel at the area under tension, k y,θ,i is the yield strength reduction factor of each steel fiber i for its (average) temperature θ, Α j is the area of each fiber j of concrete in compression and k c,θ,j is the reduction factor of concrete yield strength for each fiber j with (average) temperature θ.The f y and f c are the yield strengths of steel and concrete respectively and γ M,fi and γ Μ,fi,c are the material safety factors for fire design for steel and concrete respectively.
From equation (1) it is clear that the reduction of the yield strength of steel due to temperature is resulting reduction of the compression area A c and change of the neutral axis position.
Therefore, the moment capacity can be calculated by: ( where z i and z j are the distances of each fibre to the neutral axis. As the steel area in tension is constant and equal to the area of the bottom Tee (A bTee ) and has average temperature θ av and the temperature of concrete at the compression area is low and can be ignored, equation ( 2) can be written as: ( Where z t and z c are the distances of the tensile and compressive force from the neutral axis.
As the USFBs are shallow and have web openings, the equation 3 can be simplified by only considering the steel bottom tee section; which is the most critical part in relation to strength reduction.Therefore, equation 4 can be written as: The steel in compression is not considered at the proposed plastic analysis.The effect is minor because of the small dimensions of the upper flange in an asymmetric cross-section.For improved accuracy, equation (1) can be modified and include both concrete and steel in compression.

Effect of fire on the shear capacity of USFBs
According to [13] and [21] the shear capacity of USFBs is a combination of mechanisms: -Bearing of the concrete inside the web opening; -Friction between the concrete and both sides of the web due to the confining effect on the concrete; -Additional shear resistance of the bar reinforcement over two shear planes.
As results from Figure 7 and 8, concrete temperatures (except in a strip of a few centimeters long) are low.Also, the reinforcement bar temperature is practically not affected by fire (node 4, Figure 8).The only effect that the fire seems to have is possibly the reduction of the confinement due to high temperatures of the lower flange.
From the above numerical models it is not possible to assess the effect of fire on the shear capacity, as no shear failure occurred.In addition, the effect of horizontal shear was not assessed as the slip between the concrete and steel was not allowed in the numerical models.Given the complexity of this mechanism, further investigation is deemed necessary.

Conclusion
The paper presents a numerical investigation of the USFB behavior in fire when the lower flange is unprotected.A hypothetical fire test simulation of two typical USFBs are presented.The basic difference between the USFBs and other flooring systems is that the web is penetrated and so it is unable to produce significant moment capacity when the hot lower flange cannot provide sufficient tensile force.The difference between penetrated and not penetrated web beams depends of the web thickness.The beams without web penetration have shown increased fire resistance, between 5min and 15min, compared with the penetrated web USFBs.If the fire resistance of USFBs is compared with those of unprotected beams of same or similar cross section thickness, the USFBs have considerably improved fire resistance as the unprotected beams may not exceed the 15min.
In general, EC4-1-2 provides safe results for the fire resistance of such specimens; however USFB models with different slenderness and opening sizes need to be examined.USFBs with unprotected lower flange have a fire resistance of R40 and, as it was demonstrated, that is affected by the load factor and the deflection (thermal bowing).In order to improve the fire resistance of USFBs, the lower flange must be protected so that bowing is avoided and temperatures are reduced.Alternatively, a lower load factor might be used (or a combination of the above).
Recommendations drawn by this study emphasize that a special attention should be given to conduct fire tests for extreme designs of USFBs with in-situ as well as pre-cast slabs, in order to assess the extent of use of the current regulated specifications.Such fire tests can also be used to validate further detailed computational models simulating slim-floor steel-concrete flooring systems.Moreover, it is suggested that the shear connection systems should be assessed regarding the effect of fire, and elevated temperature push-out tests should be conducted.
A series of experimental fire tests are prepared to be conducted at the University of Ulster with those types of beams including all the structural details after the award of funding from the VCRS (Vice Chancellor Research Scholarship award for a PhD student).One of the integrated beams will have a solid web in order to be used in the investigation and documentation of temperature profiles through the unprotected composite integrated beams.The experimental data will provide the information to understand the strength loss before the failure and mechanisms of the failure modes, referential data for the calibration of the finite element models, and extended range of results; a solid basis for the definition of design rules and constructional details.

Figure 3 .
Figure 3. Analyzed beams (a) beam A, and (b) beam B

Figure 4 (
a) for structural steel and at Figure4(b) and 4(c) for concrete.For reasons of simplicity and given that no effect was noted on the results, the stress-straintemperature relationship of structural steel was used for the reinforcement bars.

Figure 4 .
Figure 4. Stress-strain temperature curves of (a) steel and concrete for (b) compression and (c) tension

Figure 5 .
Figure 5. Finite element models of the simulated USFBs (a) beam A, and (b) beam B

Figure 7 .Figure 8 .Figure 9 .
Figure 7. Temperature distribution (a) within the cross-section of beam A for 15, 30 and 45min, (b) 3D view for 120min of exposure of beam A, and (c) temperature distribution within the steel beam (beam B, 30min)

Figure 10 .
Figure 10.Mid-span deflection versus exposure duration for (a) beam A, and (b) beam B are 380 o C (lower flange) and 566 o C (web-post temperature) for beam A, and 446 o C (lower flange) and 604 o C (web-post temperature) for beam B.

Figure 12 .
Figure 12.Stress distribution of (a) a composite beam at normal temperatures, (b) when web penetrated, and (c) when web penetrated and a non linear thermal profile applies

Table 1 .
Normal temperature maximum design unity factors for the critical load combination

Table 2 .
Parameters considered in the sensitivity analysis